A power law type of time preference on intertemporal choices

Discount utility, based on utility theory, is used to study human decision behaviors under the consideration of time preference. It assumes that by means of the axiomatic system of rationality, it is possible to quantify human beings’ utilities by some explicable models for intertemporal decision making. Recent studies have been based on two basic models: the exponential and the hyperbolic discount models. These two types of model have been proved to be either too fast for discounting or too restricted for fitting human beings’ discounting behaviors. In this study, a power law discount model is proposed. Axiomatic approach is used to ascertain the existence of the power law discount utility, and empirical investigations are implemented to verify the effectiveness of the proposed model.     

An approach to group decision making under uncertainty with application to project selection

In this paper we present an approach and interactive procedure for group decision making under imprecision of expert judgements as applied to problems containing explicitly given resource constraints in particular to project selection. Alternatives (projects) are evaluated in a scale with a finite number of levels. Based on these estimates, fuzzy group preferences are determined and projects are divided into domination levels. Necessary quantities of resources are given in the form of intervals. Projects from successive levels are selected until maximum resource utilization is achieved. A numerical example is included to illustrate the proposed approach and procedure.     

An approach to group decision making based on interval multiplicative and fuzzy preference relations by using projection

This paper presents a consensus model for group decision making with interval multiplicative and fuzzy preference relations based on two consensus criteria: (1) a consensus measure which indicates the agreement between experts’ preference relations and (2) a measure of proximity to find out how far the individual opinions are from the group opinion. These measures are calculated by using the relative projections of individual preference relations on the collective one, which are obtained by extending the relative projection of vectors. First, the weights of experts are determined by the relative projections of individual preference relations on the initial collective one. Then using the weights of experts, all individual preference relations are aggregated into a collective one. The consensus and proximity measures are calculated by using the relative projections of experts’ preference relations respectively. The consensus measure is used to guide the consensus process until the collective solution is achieved. The proximity measure is used to guide the discussion phase of consensus reaching process. In such a way, an iterative algorithm is designed to guide the experts in the consensus reaching process. Finally the expected value preference relations are defined to transform the interval collective preference relation to a crisp one and the weights of alternatives are obtained from the expected value preference relations. Two numerical examples are given to illustrate the models and approaches.     

Group decision making based on intuitionistic multiplicative aggregation operators

Preference relations are the most common techniques to express decision maker’s preference information over alternatives or criteria. To consistent with the law of diminishing marginal utility, we use the asymmetrical scale instead of the symmetrical one to express the information in intuitionistic fuzzy preference relations, and introduce a new kind of preference relation called the intuitionistic multiplicative preference relation, which contains two parts of information describing the intensity degrees that an alternative is or not priority to another. Some basic operations are introduced, based on which, an aggregation principle is proposed to aggregate the intuitionistic multiplicative preference information, the desirable properties and special cases are further discussed. Choquet Integral and power average are also applied to the aggregation principle to produce the aggregation operators to reflect the correlations of the intuitionistic multiplicative preference information. Finally, a method is given to deal with the group decision making based on intuitionistic multiplicative preference relations.     

Ordering fuzzy sets over the real line: An approach based on decision making under uncertainty

The ordering of fuzzy sets over the real line is approached from the point of view of ordering intervals rather than ordering numbers. First, the maximax and maximin criteria which are commonly used for ordering intervals are expressed in terms of characteristic functions. These criteria and the Hurwicz criterion for decision making under complete ignorance are then reformulated in a manner that allows for their generalization to the fuzzy case. Transitivity is established for these ordering rules. A criterion based on the principle of diminishing marginal utility is also presented.     

An experimental study of the effect of uncertainty representation on decision making

This paper presents the results of an experiment investigating the effects of using different formats for representing uncertain attribute evaluations on decision making. Study participants make a series of hypothetical choices using six uncertainty formats - probability distributions, expected values, standard deviations, three-point (minimum-median-maximum) approximations, quantiles, and scenarios - and effects on decision making are tracked in terms of the quality of the final choice, the specific characteristics of the selected alternatives, and the difficulty experienced in making a decision. The results provide insights into how subjects make single- and multi-criteria choices in the presence of uncertainty (and some format for representing uncertainty) but in the absence of any real facilitation. The use of probability distributions appeared to overload subjects with information, leading to poorer and more difficult choices than if some intermediate level of summary was used - in particular three-point approximations or quantiles.     

An improved method on group decision making based on interval-valued intuitionistic fuzzy prioritized operators

Interval-valued intuitionistic fuzzy prioritized operators are widely used in group decision making under uncertain environment due to its flexibility to model uncertain information. However, there is a shortcoming in the existing aggregation operators (interval-valued intuitionistic fuzzy prioritized weighted average (IVIFPWA)) to deal with group decision making in some extreme situations. For example, when an expert gives an absolute negative evaluation, the operators could lead to irrational results, so that they are not effectively enough to handle group decision making. In this paper, several examples are illustrated to show the unreasonable results in some of these situations. Actually, these unreasonable cases are common for operators in dealing with product averaging, not only emerging in IVIFPWA operators. To overcome the shortcoming of these kinds of operators, an improvement of making slight adjustment on initial evaluations is provided. Numerical examples are used to show the efficiency of the improvement.     

The effects of mental model formation on group decision making: An agent‐based simulation

We investigated dynamics of group decision making on complex problems when agents can form mental models of others from discussion history. Results indicated that as the agents' memory capacity increases, the group reaches superficial consensus more easily. Surprisingly, however, the shared mental model of the problem develops only within a limited area of the problem space, because incorporating knowledge from others into one's own knowledge quickly creates local agreement on where relevant solutions are, leaving other potentially useful solutions beyond the scope of discussion. The mechanisms stifling group‐level exploration and their implications for decision making research are discussed. © 2010 Wiley Periodicals, Inc. Complexity 16: 49–57, 2011